Matrices, moments, and quadrature with applications - Golub, Gene H., (Gene Howard) (Princeton University Press, 2010)
Includes bibliographical references (pages 335-359) and index
This computationally oriented work describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms
Preliminaries; Contents; Preface; Chapter 1. Introduction; Chapter 2. Orthogonal Polynomials; Chapter 3. Properties of Tridiagonal Matrices; Chapter 4. The Lanczos and Conjugate Gradient Algorithms; Chapter 5. Computation of the Jacobi Matrices; Chapter 6. Gauss Quadrature; Chapter 7. Bounds for Bilinear Forms uT f(A)v; Chapter 8. Extensions to Nonsymmetric Matrices; Chapter 9. Solving Secular Equations; Chapter 10. Examples of Gauss Quadrature Rules; Chapter 11. Bounds and Estimates for Elements of Functions of Matrices